Texas Go Math Grade 4 Lesson 8.5 Answer Key Multiply with Regrouping

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Texas Go Math Grade 4 Lesson 8.5 Answer Key Multiply with Regrouping

Essential Question

How can you use regrouping to multiply 2-digit numbers?
Area models help to multiply large numbers, in a simpler forms using multiplication box.
Explanation:
Show the problem as the area of a rectangle, and then break that rectangle into smaller chunks for easier solving.
This method is also known as box multiplication.
Next, multiply to find the area of each smaller rectangle.
For Example;

STEP 3 Add to find the product for the whole model.
So, 16 × 19 =304
(10 x 1 tens)  ( 10 x 9 ones )  (6 x 1 tens)  ( 6 x 9 ones )
( 10 x 10 )      ( 10 x 9)           (6 x 10 )          ( 6 x 9 )
100 + 90 + 60 + 54 = 304

Unlock the Problem

By 1914, Henry Ford had streamlined his assembly line to make a Model T Ford car in 93 minutes. how many minutes did it take to make 25 Model Ts?
Estimate: 2,700
Explanation:
By using place values and regrouping to find the estimate.

Use place value and regrouping.

Multiply. 93 × 25 Estimate. 90 × 30 = _________

So, 93 × 25 is 2,325. Since _________ is close to the estimate of ___________, the answer is reasonable.
90 x 30 = 2700
So, 93 × 25 is 2,325. Since 2700 is close to the estimate of 2325, the answer is reasonable.

Math Talk

Mathematical Processes
Explain why you will get the same answer whether you multiply 93 × 25 or 25 × 93.
It shows the Commutative Property.
Explanation:
Commutative propertyThe order of the factors does not change the product.
A x B = B x A
Let’s look at an example of the commutative property:
The result of multiplying 93 x 25 will be equal to multiplying 25 x 93. Although we change the order of the factors, the result is still 2325 .

Different Ways to Multiply You can use different ways to multiply and still get the correct answer. Shawn and Patty both solved 67 × 40 correctly, but they used different ways.

Look at Shawn’s paper.

So, Shawn’s answer is 67 × 40 = 2,680.

Look at Patty’s paper.

So, Patty’s also found 67 × 40 = 2,680

Question 1.
What method did Shawn use to solve the problem?
Area models help to multiply large numbers, in a simpler forms using multiplication box.
Explanation:
Show the problem as the area of a rectangle, and then break that rectangle into smaller chunks for easier solving.
This method is also known as box multiplication.
Next, multiply to find the area of each smaller rectangle.

Question 2.
What method did Patty use to solve the problem?
She used place values and regrouping methods.
Explanation:
We can multiply 2-digit numbers by multiplying and by finding each partial products such as the tens and ones separately, then add all partial products together.

Share and Show

Question 1.
Look at the problem. Complete the sentences.

Multiply ___________ and ___________ to get 0.
Multiply ___________ and ___________ to get 1,620.
0 + 1,620 = ___________
Multiply 27 and 0 to get 0.
Multiply 27 and 60 to get 1,620.
0 + 1,620 = 1620
Explanation:
We can multiply 2-digit numbers by multiplying and by finding each partial products such as the tens and ones separately, then add all partial products together.

Math Talk

Mathematical Processes
Explain why you can omit zeros of the first partial product when you multiply 20 × 34.
Multiply 34 and 20 to get 680
0 + 680 = 680
Explanation:
As zero has no value and when we multiply any number with zero the product is zero.

Estimate. Then find the product.

Question 2.
Estimate: ____________

68 x 53 = 3,604
Estimate: 3,500
Explanation:
70 x 50 = 3,500
So, 68 × 53 is 3604.
Since 3,500 is close to the estimate of 3,604,

Question 3.
Estimate: ____________

61 x 54 = 3294
Estimate: 3300
Explanation:
60 x 55 = 3300
So, 61 × 54 is 3,294.
Since 3300 is close to the estimate of 3294,

Question 4.
Estimate: ____________

Estimate: 2,700
Explanation:
90 x 30 = 2700
So, 90 × 27 is 2430.
Since 2700 is close to the estimate of 2430,

Problem Solving

Practice: Copy and Solve Estimate. Then find the product.

Question 5.
34 × 65
Estimate: 2100
Explanation:
Estimated values of 34 is 30 and 65 is 70
So, 30 x 70 =2100

Question 6.
42 × $13 Answer:$546
Estimate: $600 Explanation: Estimated values of 42 is 40 and 13 is 15 So, 40 x 15 =600 Question 7. 60 × 17 Answer: 1,020 Estimate: 1200 Explanation: Estimated values of 17 is 20 So, 60 x 20 =1200 Question 8. 62 × 45 Answer: 2,790 Estimate: 3000 Explanation: Estimate values of 62 is 60 and 45 is 50 So, 60 x 50 = 3000 Question 9. 57 ×$98
Answer: $5,586 Estimate:$6000
Explanation:
Estimate values of 57 is 60 and 98 is 100
So, 60 x 100 = 6000

Question 10.
92 × $54 Answer:$4,968
Estimate: $4,500 Explanation: Estimate values of 92 is 90 and 54 is 50 So, 90 x 50 = 4500 Question 11. 75 × 20 Answer: 1,500 Estimate:1,500 Explanation: Estimate value 75 x 20 = 1500 As they are already rounded to the nearest tens. Question 12. 66 × 55 Answer: 3,630 Estimate: 4,200 Explanation: Estimate value of 66 is 70 and 55 is 60 So, 70 x 60 = 4200 Question 13. 73 ×$68
Answer: $4,964 Estimate:$4900
Explanation:
Estimate value of 73 is 70 and 68 is 70
So, 70 x 70 = 4900

Question 14.
72 × 40
Estimate: 2800
Explanation:
Estimate value of 72 is 70
So, 70 x 40 = 2800

Unlock the problem

Question 15.

H.O.T. Multi-Step Analyze Machine A can label 11 bottles in 1 minute. Machine B can label 12 bottles in1 minute. How many bottles can both machines label in 15 minutes?
(A) 165
(B) 180
(C) 245
(D) 345
Option(D)
Explanation:
Machine A can label 11 bottles in 1 minute.
Machine B can label 12 bottles in 1 minute.
Total bottles in 1 minute = 11 + 12 = 23
Total bottles can both machines label in 15 minutes
23 x 15 = 345 bottles.

a. What do you need to know?
I need to know total number of bottles can both the machine label in 15 minutes.

b. What numbers will you use?
I will use 11, 12 and 15 numbers.

c. Tell why you might use more than one operation to solve the problem.
To find the total number of bottles can both the machine label in 15 minutes.

d. Solve the problem.
Total bottles A + B = 11 + 12 = 23
Total bottles can both machines label in 15 minutes
23 x 15 = 345 bottles.

e. Fill in the bubble for the correct answer choice above.
Option(B) is the correct answer choice above.

Question 16.
A polo team is making 18 mallets from cane. Each mallet is 84 inches long. How many inches of cane do they use?
(A) 1,512 inches
(B) 756 inches
(C) 1,482 inches
(D) 1,412 inches
Option(A)
Explanation:
A polo team is making 18 mallets from cane.
Each mallet is 84 inches long.
Total inches of cane they use
18 x 84 = 1,512 inches.

Question 17.
A principal purchases 68 e-readers for $79 each. How much does the principal pay for the e-readers? (A)$1,088
(B) $4,802 (C)$5,372
(D) $4,372 Answer: Option(C) Explanation: A principal purchases 68 e-readers for$79 each.
Total amount paid by the principal for the e-readers.
68 x 79 = $5,372 Question 18. H.O.T. Multi-Step There are 13 students in the sticker club. Each student puts 6 stickers on each of 34 pages in their scrapbook. How many stickers are in all of the scrapbooks? (A) 546 stickers (B) 2,652 stickers (C) 2,322 stickers (D) 2,312 stickers Answer: Option(B) Explanation: There are 13 students in the sticker club. Each student puts 6 stickers on each of 34 pages in their scrapbook. Total stickers in each scrap book 34 x 6 = 204 Total stickers in all of the scrapbooks 204 x 13 = 2,652 stickers. Texas Test Prep Question 19. A toy company makes wooden blocks. A carton holds 85 blocks. How many blocks can 19 cartoons hold? (A) 1,615 (B) 1,575 (C) 1,515 (D) 850 Answer: Option(A) Explanation: A toy carton holds 85 blocks. Number of blocks can 19 cartoons hold 85 x 19 = 1,615 blocks Texas Go Math Grade 4 Lesson 8.5 Homework and Practice Answer Key Estimate. Then find the product. Question 1. Estimate _________ Answer: 3,404 Estimate: 3,500 Explanation: Estimates of 74 is 70 and 46 is 50 70 x 50 = 3,500 So, 73 × 46 is 3504. Estimate 3,500 is close to the product 3,404 So, the answer is reasonable. Question 2. Estimate _________ Answer: 364 Estimate: 300 Explanation: Estimates of 28 is 30 and 13 is 10 30 x 10 = 300 So, 28 × 13 is 364. Estimate 300 is close to the product 364 So, the answer is reasonable. Question 3. Estimate _________ Answer: 1,625 Estimate: 2,100 Explanation: Estimates of 65 is 70 and 25 is 30 70 x 30 = 2,100 So, 65 × 25 is 1,625. Estimate 2,100 is close to the product 1,625 So, the answer is reasonable. Question 4. Estimate _________ Answer: 608 Estimate: 600 Explanation: Estimates of 19 is 20 and 32 is 30 20 x 30 = 600 So, 19 × 32 is 608. Estimate 600 is close to the product 608 So, the answer is reasonable. Question 5. Estimate _________ Answer: 1,494 Estimate: 1,600 Explanation: Estimates of 83 is 80 and 18 is 20 80 x 20 = 1,600 So, 83 × 18 is 1,494. Estimate 1,600 is close to the product 1,494 So, the answer is reasonable. Question 6. Estimate _________ Answer: 2,880 Estimate: 2,800 Explanation: Estimates of 72 is 70 and 40 is already rounded to its tens place. 70 x 40 = 2,800 So, 72 × 40 is 2,880. Estimate 2,800 is close to the product 2,880 So, the answer is reasonable. Problem Solving Jill can make 14 origami boxes in an hour. Nathan can make 17 origami boxes in an hour. How many boxes can both of them make in 12 hours? Question 7. What do you need to know? Answer: I need to find number of boxes both can make in 12 hours. Question 8. What numbers will you use? Answer: Numbers used are 14, 17 and 12. Question 9. Tell why you might use more than one operation to solve the problem. Answer: Yes, more than one operation is required. Explanation: First we have to find the total number of boxes made by them in 1 hour. Then total number of boxes made in 12 hours. Question 10. Solve the problem. So, both people can make ________ boxes in 12 hours. Answer: Both can make 372 boxes. Explanation: Jill can make 14 origami boxes in an hour. Nathan can make 17 origami boxes in an hour. Total boxes both can make in 1 hour 14 + 17 = 31 Number of boxes both make in 12 hours 31 x 12 = 372 boxes Lesson Check Fill in the bubble completely to show your answer. Question 11. Bags of lemons weigh 33 pounds each. What is the total weight of 46 bags of lemons? (A) 1,308 pounds (B) 1,518 pounds (C) 1,508 pounds (D) 1,418 pounds Answer: Option(B) Explanation: Bags of lemons weigh 33 pounds each. The total weight of 46 bags of lemons 46 x 33 = 1,518 Question 12. Health club membership costs$65 a month. How much does a membership cost for 12 months?
(A) $770 (B)$690
(C) $780 (D)$775
Option(C)
Explanation:
Health club membership costs $65 a month. Total membership cost for 12 months 12 x 65 =$780

Question 13.
There are 19 players on a baseball team. Uniforms cost $74 each. How much will uniforms for the team cost? (A)$1,406
(B) $1,376 (C)$1,216
(D) $1,306 Answer: Question 14. Jason bought 39 boards that are each 12 feet long. How many feet of lumber did he buy? (A) 458 feet (B) 358 feet (C) 368 feet (D) 468 feet Answer: Option(D) Explanation: Jason bought 39 boards that are each 12 feet long. Total feet of lumber he bought 39 x 12 = 468 Question 15. Multi-Step Owners of a summer camp are buying new cots for their cabins. There are 16 cabins. Each cabin needs 6 cots. Each cot costs$92. How much will the new
(A) $8,742 (B)$9,022
(C) $8,722 (D)$8,832
Option(D)
Explanation:
There are 16 cabins.
Each cabin needs 6 cots.
16 x 6 = 96
Each cot costs \$92.
Total cost of 16 cabins
96 x 92 = 8,832

Question 16.
Multi-Step A theater has 28 rows of 38 seats downstairs and 14 rows of 26 seats upstairs. How many seats does the theater have?
(A) 1,428
(B) 1,228
(C) 1,408
(D) 1,208